The Apache 2 open-source license allows patents, does this mean it could be possible that an apache 2 open-source project would have to be removed if a company demonstrates it has a patent based on or using the project?
Any piece of software can be encumbered by patents. That is not something that is specific to the Apache license. The Apache license just acknowledges the fact and includes a patent license in addition to a copyright license.
If somebody holds a patent, then they can force you to remove your project that infringes on the patent from the internet, unless they either have given you a license to use the patented technology or you can prove in a court of law that the patent is invalid (for example because you can prove the relevant part of your software has been publicly published before the patent application was made).
The simple fact that a piece of code is licensed under the Apache license does not mean users of that code are protected from all patent claims. It is, for example, possible that a contributor makes a change that causes the code to infringe upon the patent of someone who is not involved in the project at all. That person has not suddenly given the project a patent license. Only if someone implements a patent they themselves hold can they grant a license for that patent.